Computing Chebyshev knot diagrams
Abstract
A Chebyshev curve C(a,b,c,φ) has a parametrization of the form x(t)=Ta(t); y(t)=Tb(t) ; z(t)= Tc(t + φ), where a,b,c are integers, Tn(t) is the Chebyshev polynomial of degree n and φ ∈ . When C(a,b,c,φ) has no double points, it defines a polynomial knot. We determine all possible knots when a, b and c are given.
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